83.34.7 problem 7

Internal problem ID [19349]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (H) at page 118
Problem number : 7
Date solved : Monday, March 31, 2025 at 07:09:13 PM
CAS classification : [NONE]

\begin{align*} x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \end{align*}

✗ Maple

ode:=x^2*diff(diff(y(x),x),x)+4*y(x)^2-6*y(x) = x^4*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2*D[y[x],{x,2}]+4*y[x]^2-6*y[x]==x^4*D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*Derivative(y(x), x)**2 + x**2*Derivative(y(x), (x, 2)) + 4*y(x)**2 - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - sqrt(x**2*Derivative(y(x), (x, 2)) + 4*y(x)**2 - 6*y(x))/x**2 cannot be solved by the factorable group method